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					Chaminade University of Honolulu
Physics 152 Laboratory

                           Charging and Discharging Capacitors



I. INTRODUCTION
    A. A capacitor is composed of two conductors separated by an insulator, called a
         dielectric, and has the capacity to store electrical charge and energy. A capacitor
         is charged when the two conductors have equal but opposite charges. The
         charged capacitor can hold or store this charge and since the conductors have
         opposite charges there is an electrical potential energy difference between them.
         This electrical potential energy difference increases as the stored charge
         increases. The ratio of the magnitude of stored charge (Q) to the magnitude of
         the electrical potential energy difference (V) is a positive constant for a
         capacitor. This constant is called the capacitance, C = Q/V.
    B. The units of capacitance are coulombs/volt, which is called a farad. The larger the
         capacitance the more charge the capacitor may store per given electrical
         potential energy difference. The capacitance is a function of several factors
           1) the geometry of the conductors
           2) the insulating material, the dielectric, between the conductors
                  (a) compared to the electric field E0 between the conductors that are
                     separated by a vacuum, a dielectric is characterized by a (dielectric)
                     constant, , that reflects a decrease in the electric field between the
                     conductors: E = E0/, when the dielectric, instead of vacuum,
                     separates the conductors. (Note that  is greater than 1 for electrically
                     insulating materials, and that it is defined as 1 for a vacuum). The
                     decrease in electric field is proportional to a decrease in electrical
                     potential energy difference V (versus V0, that is V = V0/) between
                     the conductors. Basically, the dielectric undergoes polarization
                     induced alignment of dipoles that results in a shielding of the electric
                     field between the conductors. Overall, the capacitance increases with
                     the insertion of a dielectric versus vacuum. (See Table 20-1, p. 665)
                          i. Insertion of a dielectric into a charged capacitor, that is the
                             capacitor is disconnected from a battery source after being
                             charged, decreases V (versus V0) without affecting the stored
                             charge Q. Therefore, since C = Q/V, C has to increase-by the
                             factor .
                          ii. Insertion of a dielectric into a capacitor that is being charged,
                             that is the capacitor containing the dielectric is connected to a
                             battery source, would require more charge Q (versus Q0, that is
                             Q = Q0*) to build up on the conductors, in order to reach the
                             same potential V as that of the battery. Therefore, since C =
                             Q/V, C has to increase-by the factor .
                  (b) There is maximum value of electric field, called the dielectric
                     strength, to which a dielectric can withstand without dissociation on
                     an atomic level. If this value of electric field is surpassed, the

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Chaminade University of Honolulu
Physics 152 Laboratory

                           Charging and Discharging Capacitors



                    dielectric will break; the process called dielectric breakdown. (See
                    Table 20-2, p.667)
    C. The work necessary to charge a capacitor, comes from the energy of a voltage
         source, (e.g. the chemical energy of a battery), and is converted to electrical
         potential energy within the electric field of the capacitor; the field between the
         conductors. Note that a capacitor can build up an electrical potential energy
         difference equal to that of the charging source, but that it can discharge its stored
         energy must faster, which leads to a larger power output than possible with the
         voltage source.
    D. Charging a capacitor requires charging each conductor individually, since ideally
         charge does not travel through the insulating material between the conductors of
         a capacitor
           1) The connection of a capacitor to a battery source nearly instantaneously
               charges the conductors of the capacitor to an electrical potential energy
               difference of the same magnitude and polarity as that of the battery. Note
               by the definition of capacitance, that the total charge accumulated on the
               capacitor is Q = CV or Q = C.
           2) The addition of resistors in series with the capacitor of the circuit increases
               the charging time required for the capacitor. Furthermore, the electrical
               potential energy drop across the resistor (see Laboratory Experiment
               Ohmic resistors) causes the electrical potential energy drop across the
               capacitor to be less than that of the battery source.
                 (a)  - IR – Q/C = 0 (Kirchoff’s voltage loop rule)
                 (b) I0 =  / R (At the instant the RC elements are connected to the
                    battery, there is not yet any Q on the capacitor. At this time, the
                    electrical potential energy drop is only across the resistor.)
                 (c) Q = C(Later when the capacitor becomes fully charged, there is no
                    longer any current flowing: I=0. The electrical potential energy drop
                    is entirely across the capacitor.)
    E. Mathematical operations on the equation of D.2)(a) yields analytical expressions
         for charging the capacitor.




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Physics 152 Laboratory

                           Charging and Discharging Capacitors



    F. For the discharging of a charged capacitor, we must remove the battery from the
         circuit and substitute a switch that is left open. In this case, we are left with a
         charged capacitor with a voltage drop of Qmax/C but zero electrical potential
         energy drop across the resistor because there is no current flowing. Closing the
         switch will allow the capacitor to discharge through the resistor. At any time
         during this process, the current in the circuit is I and is equal to the rate of
         decrease of charge Q on the capacitor. This current then puts a potential
         electrical energy difference across the resistor. At any given time the potential
         electrical energy differences across these two circuit elements are equal: IR =
         Q/C (Kirchoff’s voltage loop rule). Mathematical operations on this equation
         yield analytical expressions for discharging the capacitor.




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Chaminade University of Honolulu
Physics 152 Laboratory

                           Charging and Discharging Capacitors



II. OUTLINE
    A. Form an RC circuit with one voltage source, one capacitor, one resistor and a
         single-pole, double-throw switch.
    B. Measure and record voltage drops across the capacitor during charging and
         discharging.
    C. Observer current in the circuit, particularly direction during these processes as well
         as the voltage drop across the resistor.

III. PROCEDURE
     A. Setup the RC circuit as directed with an ammeter and voltmeter inserted.
     B. Use the single-pole, double-throw switch to charge the capacitor through the
          resistor with the battery.
            1) Note the direction of current.
            2) Note the voltage drop across the resistor.
            3) Record in Table 1 of the Data Sheet the buildup of the electrical potential
                 energy difference across the capacitor every 5-10s until the capacitor’s
                 electrical potential energy difference asymptotes off to a constant value.
     C. Use the single-pole, double-throw switch to discharge the capacitor through the
          resistor and breaking contact with the battery.
            1) Note the direction of current.
            2) Note the voltage drop across the resistor.
            3) Record in Table 1 of the Data Sheet the decrease of voltage across the
                 capacitor every 5-10s until the capacitor’s electrical potential energy
                 difference asymptotes off to a constant value.
     D. Determining the RC time constant.
            1) Based on the data of Table 1 in the Data Sheet, calculate the values of  - V
                 and ln( - V) as outlined in the INTRODUCTION for charging of a
                 capacitor.
                   (a) Record these values in Table 1 of the Results Sheet.
                   (b) Plot this data to determine the RC time constant.
                   (c) Compare to the given values of R= and C= as a percent error. (Note
                      that resistance can be expressed as volts/coulombs/seconds and that
                      capacitance can be expressed as coulombs/volts, so that the product is
                      in units of time.)
            2) Based on the data of Table 1 in the Data Sheet, calculate the values of ln
                 V(t) and of ln Vmax as outlined in the INTRODUCTION for discharging of
                 a capacitor.
                   (a) Record these values in the Table 2 of the Results Sheet.
                   (b) Plot this data to determine the RC time constant.
                   (c) Compare to the given values of R= and C= as a percent error.



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